Finite Group Databasebeta

← #11810342

Subgroups — #11810342

Order 1152.

1695 conjugacy classes of subgroups.

The subgroup lattice has 1079 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#882C211yesmaximal, characteristic
2C2×#63969C211yesmaximal, characteristic, complemented
3C2×D3×#217C211yesmaximal, characteristic, complemented
4C2×#63898C211yesmaximal, characteristic, complemented
5#10592643C211yesmaximal, characteristic, complemented
6C3×#4953C211yesmaximal, characteristic, complemented
7#10591708C211yesmaximal, characteristic, complemented
8#10591706C211yesmaximal, characteristic, complemented
9#10591376C211yesmaximal, characteristic, complemented
10#10591376C211yesmaximal, characteristic, complemented
11#10591373C211yesmaximal, characteristic, complemented
12#10591369C211yesmaximal, characteristic, complemented
13#10591324C211yesmaximal, characteristic, complemented
14#10591302C211yesmaximal, characteristic, complemented
15#10591287C211yesmaximal, characteristic, complemented
16#82585—31nomaximal
17#77669—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic, complemented
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C2×#3750C2211yescharacteristic, complemented
29C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
35C3×#882—24no—
36#63969—24no—
37D3×#217—24no—
38C2×#3724C2211yescharacteristic, complemented
39C2×#3724C2211yescharacteristic, complemented
40C2×Dic3⋊Dic3C2211yescharacteristic, complemented
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
48C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
49C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
50#63898—24no—
51#63658C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55C3×C3⋊#95C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×C3×#120—31no—
58C22×#217—31no—
59C2×#935—31no—
60C2×D4×Dic3—31no—
61C2×#893—31no—
62C2×#883—31no—
63C2×#882D311yescharacteristic
64C2×D3×C22⋊C4—31no—
65C3×#397—31no—
66#5247—31no—
67#5222—31no—
68#5222—31no—
69#5220—31no—
70#5220—31no—
71#4993—31no—
72#4959—31no—
73#4955—31no—
74#4953D311yescharacteristic, complemented
75#4949—31no—
76#4946—31no—
77#4944—31no—
78#4944—31no—
79#4944—31no—
80#4944—61no—
81#4942—31no—
82#4672—31no—
83#4670—31no—
84#4668—31no—
85#4667—31no—
86#4665—31no—
87#4665—31no—
88C24×C32C2311yescharacteristic
89C23×C3×D3—22no—
90C23×C3×D3—22no—
91C23×C3×D3—22no—
92C23×C3×D3—22no—
93C23×C3×D3—22no—
94C23×C3×D3—41no—
95C23×C3×D3—41no—
96C23×C3×D3C2311yescharacteristic
97C23×C3×D3C2311yescharacteristic
98C23×C3×D3C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C2×C3×#67—41no—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C2×C3×D12—22no—
114C2×C3×D12—22no—
115C2×C3×D12—22no—
116C2×C3×D12—22no—
117C2×C3×D12—41no—
118C2×C3×D12D414yes—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121C2×D3×Dic3—22no—
122C2×D3×Dic3—22no—
123C2×D3×Dic3—22no—
124C2×D3×Dic3—22no—
125C2×D3×Dic3—41no—
126C2×D3×Dic3—41no—
127C2×D3×Dic3—41no—
128C32×C22⋊C4—22no—
129#3757—41no—
130#3757D414yescomplemented
131#3750—41no—
132C4×C3⋊Dic3—22no—
133C3×#217—22no—
134C3×#217—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—22no—
137C3×C4⋊Dic3—22no—
138#3724—22no—
139#3724—41no—
140Dic3⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—41no—
149(C2×D3)⋊Dic3—41no—
150#2418—91noSylow
151C25×C3—31no—
152C24×D3C2×D311yescharacteristic
153C22×C3×D4—31no—
154C22×C3×D4—31no—
155C22×C3×D4—31no—
156C22×#67C2×D311yescharacteristic
157C23×Dic3—31no—
158C23×Dic3—31no—
159C23×Dic3—31no—
160C22×D12C2×D311yescharacteristic
161C22×D12C2×D311yescharacteristic
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C3×#120—64no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C22⋊C4—21no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4C2×D311yescharacteristic
173C2×C3×C22⋊C4C2×D311yescharacteristic
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—31no—
186C2×#217—31no—
187C2×#217—61no—
188C2×#217—61no—
189C2×#217—64no—
190C2×#217C2×D311yescharacteristic
191C2×#217C2×D311yescharacteristic
192#935—64no—
193D4×Dic3—64no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4C2×D311yescharacteristic
204C2×(C2×D3)⋊C4C2×D311yescharacteristic
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3C2×D311yescharacteristic, complemented
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—61no—
215C2×C4×Dic3—31no—
216C2×C4×Dic3—31no—
217C2×C4×Dic3—61no—
218#893—64no—
219#883—64no—
220#882—24no—
221D3×C22⋊C4—64no—
222C3×#95—31no—
223C3×#95—31no—
224C3×#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—61no—
232C3⋊#95—61no—
233C3⋊#95C2×D311yescharacteristic, complemented
234C3⋊#95C2×D311yescharacteristic, complemented
235C3⋊#95C2×D311yescharacteristic, complemented
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32C2×D412yes—
243C23×C32C2411yescharacteristic
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—28no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—44no—
262C22×C3×D3—44no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3—44no—
266C22×C3×D3—44no—
267C22×C3×D3C2×D412yes—
268C22×C3×D3C2×D412yes—
269C22×C3×D3#4112yes—
270C22×C3×D3#4112yes—
271C22×C3×D3#4112yes—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4C2×D412yes—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3—21no—
287C2×C3⋊Dic3—21no—
288C2×C3⋊Dic3C2×D412yes—
289C2×C3⋊Dic3C2×D412yes—
290C3×#67—44no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C3×D12—28no—
307C3×D12—44no—
308D3×Dic3—44no—
309D3×Dic3—44no—
310D3×Dic3—44no—
311C2×#123—91no—
312C2×#120—31no—
313C2×C4×D4—91no—
314C22×C22⋊C4—91no—
315#399—91no—
316#397—31no—
317#394—91no—
318#394—91no—
319#388—91no—
320#388—91no—
321#386—91no—
322#386—91no—
323#385—91no—
324#380—91no—
325#379—91no—
326C24×C3—21no—
327C24×C3—31no—
328C24×C3—31no—
329C24×C3—31no—
330C24×C3—62no—
331C24×C3—62no—
332C24×C3—62no—
333C24×C3—62no—
334C24×C3—62no—
335C24×C3—121no—
336C24×C3—121no—
337C24×C3C22×D311yescharacteristic
338C24×C3C22×D311yescharacteristic
339C23×D3—22no—
340C23×D3—22no—
341C23×D3—22no—
342C23×D3—22no—
343C23×D3—22no—
344C23×D3—41no—
345C23×D3—41no—
346C23×D3C22×D311yescharacteristic
347C23×D3C22×D311yescharacteristic
348C23×D3C22×D311yescharacteristic
349C2×C3×D4—34no—
350C2×C3×D4—62no—
351C2×C3×D4—62no—
352C2×C3×D4—62no—
353C2×C3×D4—62no—
354C2×C3×D4—62no—
355C2×C3×D4—62no—
356C2×C3×D4—121no—
357C2×C3×D4—121no—
358C22×C3×C4—21no—
359C22×C3×C4—21no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C2×#67—22no—
370C2×#67—22no—
371C2×#67—41no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—61no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—61no—
384C22×Dic3—62no—
385C22×Dic3—62no—
386C22×Dic3—62no—
387C22×Dic3—62no—
388C22×Dic3—62no—
389C22×Dic3—62no—
390C22×Dic3—121no—
391C22×Dic3—121no—
392C22×Dic3—121no—
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C2×D12—22no—
399C2×D12—22no—
400C2×D12—22no—
401C2×D12—22no—
402C2×D12—41no—
403C2×D12#6714yes—
404C2×C4×D3—62no—
405C2×C4×D3—62no—
406C2×C4×D3—62no—
407C2×C4×D3—62no—
408C2×C4×D3—62no—
409C2×C4×D3—62no—
410C2×C4×D3—121no—
411C2×C4×D3—121no—
412C2×C4×D3—121no—
413C3×C4⋊C4—62no—
414C3×C22⋊C4—22no—
415C3×C22⋊C4—22no—
416C3×C22⋊C4—42no—
417C3×C22⋊C4—62no—
418C3×C22⋊C4—62no—
419C3×C22⋊C4—62no—
420C3×C22⋊C4—62no—
421#217—22no—
422#217—22no—
423#217—34no—
424#217—34no—
425#217—64no—
426#217—62no—
427#217—62no—
428#217—62no—
429#217—62no—
430#217—62no—
431#217—62no—
432#217—62no—
433#217—121no—
434#217—121no—
435#217—121no—
436#217—121no—
437#217—122no—
438(C2×D3)⋊C4—22no—
439(C2×D3)⋊C4—22no—
440(C2×D3)⋊C4—62no—
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—121no—
448(C2×D3)⋊C4—121no—
449C4⋊Dic3—22no—
450C4⋊Dic3—62no—
451Dic3⋊C4—62no—
452Dic3⋊C4—62no—
453Dic3⋊C4—62no—
454Dic3⋊C4—121no—
455Dic3⋊C4—121no—
456Dic3⋊C4—121no—
457Dic3⋊C4—121no—
458Dic3⋊C4—122no—
459C4×Dic3—62no—
460C4×Dic3—62no—
461C4×Dic3—122no—
462C22×C32—22no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32C22×D411yescharacteristic
470C22×C32C22×D411yescharacteristic
471C22×C32C2×#4111yescharacteristic
472C22×C32C2×#4111yescharacteristic
473C22×C32C2×#4111yescharacteristic
474C22×C32H(5,𝔽2)11yescharacteristic
475C22×C32H(5,𝔽2)11yescharacteristic
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—416no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3#12314yescomplemented
498C32×C4—22no—
499C32×C4—41no—
500C3⋊Dic3—22no—
501C3⋊Dic3—22no—
502C3⋊Dic3—41no—
503C3⋊Dic3—41no—
504C3×Dic3—41no—
505C3×Dic3—41no—
506C3×Dic3—41no—
507C3×Dic3—41no—
508C3×Dic3—41no—
509C25—31no—
510C22×D4—31no—
511C22×D4—31no—
512C22×D4—31no—
513C23×C4—91no—
514C23×C4—91no—
515C23×C4—91no—
516#123—184no—
517#120—64no—
518C4×D4—184no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—91no—
521C2×C4⋊C4—91no—
522C2×C4⋊C4—91no—
523C2×C4⋊C4—91no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—31no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—91no—
529C2×C22⋊C4—91no—
530C2×C22⋊C4—91no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—184no—
540C2×C22⋊C4D3211yescharacteristic
541C2×C42—91no—
542#95—31no—
543#95—31no—
544#95—31no—
545#95—91no—
546#95—91no—
547#95—91no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—22no—
562C23×C3—32no—
563C23×C3—32no—
564C23×C3—32no—
565C23×C3—32no—
566C23×C3—32no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—41no—
573C23×C3—68no—
574C23×C3—61no—
575C23×C3—61no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3—61no—
579C23×C3—61no—
580C23×C3—61no—
581C23×C3—61no—
582C23×C3—61no—
583C23×C3—61no—
584C23×C3—61no—
585C23×C3—61no—
586C23×C3—61no—
587C23×C3—61no—
588C23×C3—61no—
589C23×C3—61no—
590C23×C3—124no—
591C23×C3—124no—
592C23×C3—124no—
593C23×C3—124no—
594C23×C3—124no—
595C23×C3—124no—
596C23×C3D3×D412yes—
597C23×C3D3×D412yes—
598C23×C3C23×D311yescharacteristic
599C23×C3C23×D311yescharacteristic
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—28no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—21no—
615C22×D3—21no—
616C22×D3—21no—
617C22×D3—44no—
618C22×D3—44no—
619C22×D3—44no—
620C22×D3—44no—
621C22×D3—44no—
622C22×D3—44no—
623C22×D3#23712yes—
624C22×D3#23712yes—
625C22×D3#23712yes—
626C22×D3C2×#6712yes—
627C22×D3C2×#6712yes—
628C3×D4—68no—
629C3×D4—124no—
630C3×D4—124no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—22no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4D3×D412yes—
663C2×C3×C4C2×#6712yes—
664#67—44no—
665C2×Dic3—21no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—21no—
671C2×Dic3—21no—
672C2×Dic3—21no—
673C2×Dic3—21no—
674C2×Dic3—21no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—32no—
681C2×Dic3—32no—
682C2×Dic3—32no—
683C2×Dic3—32no—
684C2×Dic3—62no—
685C2×Dic3—62no—
686C2×Dic3—61no—
687C2×Dic3—61no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—61no—
694C2×Dic3—62no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—121no—
708C2×Dic3—121no—
709C2×Dic3—121no—
710C2×Dic3—121no—
711C2×Dic3—121no—
712C2×Dic3—121no—
713C2×Dic3—121no—
714C2×Dic3—121no—
715C2×Dic3—121no—
716C2×Dic3—124no—
717C2×Dic3—124no—
718C2×Dic3—124no—
719D12—28no—
720D12—44no—
721C4×D3—124no—
722C4×D3—124no—
723C4×D3—124no—
724C2×C32—42no—
725C2×C32C2×#12311yescharacteristic
726C2×C32#52511yescharacteristic
727C2×C32#53811yescharacteristic
728C2×C32D4211yescharacteristic
729C2×C32#54611yescharacteristic
730C2×C32#54611yescharacteristic
731C2×C32#55111yescharacteristic
732C3×D3—24no—
733C3×D3—42no—
734C3×D3—42no—
735C24—31no—
736C24—31no—
737C24—31no—
738C24—62no—
739C24—62no—
740C24—62no—
741C24—62no—
742C24—62no—
743C24—121no—
744C24—121no—
745C24C2×D3211yescharacteristic
746C2×D4—34no—
747C2×D4—62no—
748C2×D4—62no—
749C2×D4—62no—
750C2×D4—62no—
751C2×D4—62no—
752C2×D4—62no—
753C2×D4—121no—
754C2×D4—121no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—91no—
761C22×C4—91no—
762C22×C4—91no—
763C22×C4—91no—
764C22×C4—182no—
765C22×C4—182no—
766C22×C4—182no—
767C22×C4—182no—
768C22×C4—182no—
769C22×C4—182no—
770C22×C4—361no—
771C22×C4—361no—
772C22×C4—361no—
773C22×C4C2×D3211yescharacteristic
774C22×C4C2×D3211yescharacteristic
775C4⋊C4—62no—
776C4⋊C4—182no—
777C4⋊C4—182no—
778C4⋊C4—361no—
779C4⋊C4—361no—
780C22⋊C4—22no—
781C22⋊C4—62no—
782C22⋊C4—62no—
783C22⋊C4—62no—
784C22⋊C4—62no—
785C22⋊C4—94no—
786C22⋊C4—182no—
787C22⋊C4—182no—
788C22⋊C4—182no—
789C22⋊C4—182no—
790C22⋊C4—182no—
791C22⋊C4—182no—
792C22⋊C4—182no—
793C22⋊C4—361no—
794C22⋊C4—361no—
795C22⋊C4—361no—
796C42—182no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—22no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—34no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—42no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—62no—
828C22×C3—62no—
829C22×C3—62no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—81no—
835C22×C3—81no—
836C22×C3—81no—
837C22×C3—81no—
838C22×C3—1216no—
839C22×C3—121no—
840C22×C3—121no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3—121no—
847C22×C3C2×D3×D411yescharacteristic
848C22×C3C2×D3×D411yescharacteristic
849C22×C3C2×D3×D411yescharacteristic
850C22×C3C2×#23711yescharacteristic
851C22×C3C2×#23711yescharacteristic
852C22×C3C2×#23711yescharacteristic
853C22×C3#100411yescharacteristic
854C22×C3#100411yescharacteristic
855C22×C3D3×#4111yescharacteristic
856C22×C3D3×#4111yescharacteristic
857C22×C3D3×#4111yescharacteristic
858C22×C3#100911yescharacteristic
859C22×C3#100911yescharacteristic
860C22×C3C22×#6711yescharacteristic
861C2×D3—22no—
862C2×D3—22no—
863C2×D3—22no—
864C2×D3—22no—
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—416no—
874C2×D3—41no—
875C2×D3—41no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—41no—
880C2×D3—41no—
881C2×D3—41no—
882C2×D3#93514yescomplemented
883C3×C4—22no—
884C3×C4—22no—
885C3×C4—42no—
886C3×C4—41no—
887C3×C4—41no—
888C3×C4—81no—
889C3×C4—121no—
890C3×C4—121no—
891C3×C4—121no—
892C3×C4—121no—
893C3×C4—121no—
894Dic3—41no—
895Dic3—41no—
896Dic3—41no—
897Dic3—41no—
898Dic3—41no—
899Dic3—62no—
900Dic3—62no—
901Dic3—62no—
902Dic3—62no—
903Dic3—122no—
904Dic3—122no—
905Dic3—122no—
906Dic3—121no—
907Dic3—121no—
908Dic3—121no—
909Dic3—121no—
910Dic3—241no—
911C32#241811yescharacteristic, complemented, Sylow
912C23—21no—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—32no—
919C23—32no—
920C23—32no—
921C23—32no—
922C23—32no—
923C23—68no—
924C23—61no—
925C23—61no—
926C23—61no—
927C23—61no—
928C23—61no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—61no—
933C23—61no—
934C23—61no—
935C23—61no—
936C23—61no—
937C23—61no—
938C23—61no—
939C23—61no—
940C23—124no—
941C23—124no—
942C23—124no—
943C23—124no—
944C23—124no—
945C23—124no—
946C23#380212yes—
947C23C22×D3211yescharacteristic
948D4—68no—
949D4—124no—
950D4—124no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—61no—
957C2×C4—61no—
958C2×C4—61no—
959C2×C4—61no—
960C2×C4—61no—
961C2×C4—61no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—61no—
966C2×C4—61no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—92no—
972C2×C4—92no—
973C2×C4—181no—
974C2×C4—181no—
975C2×C4—181no—
976C2×C4—181no—
977C2×C4—181no—
978C2×C4—181no—
979C2×C4—181no—
980C2×C4—181no—
981C2×C4—181no—
982C2×C4—181no—
983C2×C4—364no—
984C2×C4—364no—
985C2×C4—364no—
986C2×C4D3×#6712yes—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—21no—
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—42no—
995C2×C3—42no—
996C2×C3—64no—
997C2×C3—82no—
998C2×C3—122no—
999C2×C3—122no—
1000C2×C3#558611yescharacteristic
1001C2×C3#558711yescharacteristic
1002C2×C3#559111yescharacteristic
1003C2×C3#559311yescharacteristic
1004C2×C3#560911yescharacteristic
1005C2×C3D3×#12311yescharacteristic
1006C2×C3#565411yescharacteristic
1007C2×C3#565611yescharacteristic
1008C2×C3#567611yescharacteristic
1009C2×C3#570411yescharacteristic
1010C2×C3#570511yescharacteristic
1011C2×C3C2×#93511yescharacteristic
1012C2×C3D4×#6711yescharacteristic
1013C2×C3#580611yescharacteristic
1014D3—24no—
1015D3—42no—
1016D3—42no—
1017C22—22no—
1018C22—22no—
1019C22—22no—
1020C22—34no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—62no—
1026C22—62no—
1027C22—62no—
1028C22—62no—
1029C22—62no—
1030C22—62no—
1031C22—62no—
1032C22—62no—
1033C22—62no—
1034C22—62no—
1035C22—62no—
1036C22—62no—
1037C22—1216no—
1038C22—121no—
1039C22—121no—
1040C22—121no—
1041C22—121no—
1042C22—121no—
1043C22—121no—
1044C22—121no—
1045C22—121no—
1046C22C2×#380211yescharacteristic
1047C22#6430711yescharacteristic
1048C22D3×#23711yescharacteristic
1049C22D3×#23711yescharacteristic
1050C22D3×#23711yescharacteristic
1051C22#6431411yescharacteristic
1052C22C2×D3×#6711yescharacteristic
1053C4—22no—
1054C4—41no—
1055C4—121no—
1056C4—121no—
1057C4—121no—
1058C4—121no—
1059C4—121no—
1060C4—182no—
1061C4—182no—
1062C4—361no—
1063C4—361no—
1064C3—21no—
1065C3#7766911yescharacteristic, complemented
1066C3#8258511yescharacteristic, complemented
1067C2—42no—
1068C2—64no—
1069C2—122no—
1070C2—122no—
1071C2#1059408211yescharacteristic
1072C2#1059411511yescharacteristic
1073C2#1059412611yescharacteristic
1074C2#1059429411yescharacteristic
1075C2#1059506911yescharacteristic
1076C2D3×#93511yescharacteristic
1077C2#1059522911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×C3×#882C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#63969C2semidirect
3. C2×D3×#217C2semidirect
4. C2×#63898C2semidirect
5. #10592643C2semidirect
6. C3×#4953C2semidirect
7. #10591708C2semidirect
8. #10591706C2semidirect
9. #10591376C2semidirect
10. #10591376C2semidirect
11. #10591373C2semidirect
12. #10591369C2semidirect
13. #10591324C2semidirect
14. #10591302C2semidirect
15. #10591287C2semidirect
24. C22×D3×Dic3C22semidirect
28. C2×#3750C22semidirect
29. C2×C4×C3⋊Dic3C22semidirect
34. C2×C3×C4⋊Dic3C22semidirect
38. C2×#3724C22semidirect
39. C2×#3724C22semidirect
40. C2×Dic3⋊Dic3C22semidirect
47. C2×(C2×D3)⋊Dic3C22semidirect
48. C2×(C2×D3)⋊Dic3C22semidirect
49. C2×(C2×D3)⋊Dic3C22semidirect
51. #63658C22semidirect
52. #63658C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. C3×C3⋊#95C22semidirect
56. #63579C22semidirect
74. #4953D3semidirect
130. #3757D4semidirect
206. C2×C4⋊Dic3C2×D3semidirect
233. C3⋊#95C2×D3semidirect
234. C3⋊#95C2×D3semidirect
235. C3⋊#95C2×D3semidirect
497. C2×C3×D3#123semidirect
882. C2×D3#935semidirect
911. C32#2418semidirect
1065. C3#77669semidirect
1066. C3#82585semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#8822
C2×#639692
C2×D3×#2172
C2×#638982
#105926432
C3×#49532
#105917082
#105917062
#105913762
#105913732
#105913692
#105913242
#105913022
#105912872
#825853
#776693